A Cross-Sectional Investigation of Students' Reasoning About Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility
A Cross-Sectional Investigation of Students' Reasoning About Integer Addition and Subtraction: Ways of Reasoning, Problem Types, and Flexibility
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学生整数加减法推理的横断面调查：推理方式、问题类型和灵活性
DOI：
10.5951/jresematheduc.49.5.0575
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发表时间：
2018
影响因子：
2.8
通讯作者：
Bonnie P. Schappelle
中科院分区：
文献类型：
--
作者：
Lisa L. C. Lamb;J. Bishop;Radolph A. Philipp;Ian Whitacre;Bonnie P. Schappelle
在一项横断面研究中，对160名二、四、七和十一年级学生进行了关于他们在解决整数加减法开数句问题时的推理的访谈。我们将之前开发的5种推理方式（WoRs）框架应用于我们的数据集，以描述参与者组内和跨参与者组的模式。我们对WoR的分析也导致了3种问题类型的识别：积极变化，全否定和违反直觉。我们发现，问题类型影响学生的表现，往往会引起不同的推理方式。我们发现，那些对负数有更多经验的人比那些经验较少的人更灵活地使用WoRs，并且灵活性与准确性相关。我们为教育工作者提供3种类型的资源：（a）WoR和问题类型框架，（B）整数加减灵活性的表征，以及（c）整数学习轨迹的发展。
In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-numbersentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis of the WoRs also led to the identification of 3 problem types: change-positive, all-negatives, and counterintuitive. We found that problem type influenced student performance and tended to evoke a different way of reasoning. We showed that those with more experience with negative numbers use WoRs more flexibly than those with less experience and that flexibility is correlated with accuracy. We provide 3 types of resources for educators: (a) WoRs and problem-types frameworks, (b) characterization of flexibility with integer addition and subtraction, and (c) development of a trajectory of learning about integers.